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EVM: A Fast Alternative to the EM Algorithm with Application to Gaussian Mixture Models EVM:一种快速替代EM算法的高斯混合模型应用
ERN: Model Construction & Estimation (Topic) Pub Date : 2020-06-01 DOI: 10.2139/ssrn.3615408
Mark Britten-Jones
{"title":"EVM: A Fast Alternative to the EM Algorithm with Application to Gaussian Mixture Models","authors":"Mark Britten-Jones","doi":"10.2139/ssrn.3615408","DOIUrl":"https://doi.org/10.2139/ssrn.3615408","url":null,"abstract":"This article presents EVM (Expectation-Variance-Maximization) — an alternative algorithm to the EM algorithm that can reduce training times dramatically. The new approach belongs to the class of general Newton algorithms and is applicable in most situations where the EM algorithm is currently used so is useful for a wide variety of estimation problems. Two identities associated with the EM algorithm provide analytical expressions for the gradient and Hessian matrices used in the EVM algorithm. The new algorithm is demonstrated for parameter estimation in Gaussian Mixture Models. Simulations show that training times are reduced significantly and in difficult cases more than 100-fold in comparison to the EM algorithm.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122763736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spurious Relationships For Nearly Non-stationary Series 近似非平稳级数的伪关系
ERN: Model Construction & Estimation (Topic) Pub Date : 2020-04-30 DOI: 10.3390/jrfm14080366
Yushan Cheng, Yongchang Hui, M. McAleer, W. Wong
{"title":"Spurious Relationships For Nearly Non-stationary Series","authors":"Yushan Cheng, Yongchang Hui, M. McAleer, W. Wong","doi":"10.3390/jrfm14080366","DOIUrl":"https://doi.org/10.3390/jrfm14080366","url":null,"abstract":"Literature shows that the regression of independent and (nearly) nonstationary time series could result in spurious outcomes. In this paper, we conjecture that under some situations, the regression of two independent and nearly non-stationary series does not have any spurious problem at all. To check whether our conjecture holds, we set up several situations and conduct simulations to justify our conjecture. Our simulations show that under some situations, the chance that the regressions being spurious is very high for all the cases simulated in our paper. Nonetheless, under some other situations, our simulation shows that the rejection rates are much smaller than the 5% level of significance for all the cases simulated in our paper, implying that our conjecture could hold under some situations that regression of two independent and nearly non-stationary series does not have any spurious problem at all.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128320491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Calibration of Local Correlation Models. Notice to Skeptics of Particle Methods: With the Diffusion Implied Kernel, You Will Have No More Excuses! 局部相关模型的校正。对粒子方法持怀疑态度的人注意:有了扩散隐含核，你就没有借口了!
ERN: Model Construction & Estimation (Topic) Pub Date : 2020-04-01 DOI: 10.2139/ssrn.3590838
Rida Mahi
{"title":"Calibration of Local Correlation Models. Notice to Skeptics of Particle Methods: With the Diffusion Implied Kernel, You Will Have No More Excuses!","authors":"Rida Mahi","doi":"10.2139/ssrn.3590838","DOIUrl":"https://doi.org/10.2139/ssrn.3590838","url":null,"abstract":"In this paper we compare three ways of taking into account the basket skew by using a LVLC (Local Volatility Local Correlation) model. The two first methods were already presented in Langnau (2009) and Guyon and Henry-Labordère (2012). The third method, which is the main result of this paper, reduces the number of used particles by a factor of 10 and was inspired from Muguruza (2019).<br><br>This article is organized as follows. After a paragraph where we introduce the hypothesis and notations, we briefly present the final objective of the calibration. We then propose 3 solutions which are special cases of the (Guyon, 2017) framework: <br><br>• Method 1 does not require a conditional expectation calculation (and therefore has no calibration phase) is presented here for comparison <br><br>• Method 2 is based on the classical calculation of conditional expectations by choosing a Kernel and a bandwidth parameter <br><br>• Method 3 calculates the conditional expectations required by method 2 using the diffusion implied kernel<br><br>Then we move on to numerical results paragraph where we present honestly the benefits of the alternative method followed by the appendices where we provide the proofs of the propositions and the details of the calculations allowing to easily implement the diffusion implied kernel.<br>","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130368316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Moment Diagnostics and Quasi-Maximum Likelihood Estimation for the Stochastic Frontier Model 随机前沿模型的矩诊断和拟极大似然估计
ERN: Model Construction & Estimation (Topic) Pub Date : 2019-12-31 DOI: 10.2139/ssrn.3528423
A. Papadopoulos, Christopher F. Parmeter
{"title":"Moment Diagnostics and Quasi-Maximum Likelihood Estimation for the Stochastic Frontier Model","authors":"A. Papadopoulos, Christopher F. Parmeter","doi":"10.2139/ssrn.3528423","DOIUrl":"https://doi.org/10.2139/ssrn.3528423","url":null,"abstract":"The distributional specifications for the composite regression error term most often used in Stochastic Frontier Analysis (SFA) are inherently bounded as regards their skewness and excess kurtosis coefficients. These bounds provide simple diagnostic tools and model selection/rejection criteria for empirical studies which appear to have been overlooked by practitioners. We derive general expressions for the skewness and excess kurtosis of the composed error term in the stochastic frontier model based on the ratio of standard deviations of the two separate error components as well as theoretical ranges for the most popular empirical specifications. Simulation results are presented to detail the small-sample effects as well as to speak towards the practical relevance of these diagnostic tools and the consequences of misspecification. These insights lead us to examine quasi-maximum likelihood estimation (QMLE) of the ubiquitous Normal-Half Normal stochastic frontier model and the properties of the Skew-Normal QMLE, more generally.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122200019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Realized Volatility Estimator Under Liquidity Effects 流动性效应下的已实现波动估计
ERN: Model Construction & Estimation (Topic) Pub Date : 2019-12-26 DOI: 10.2139/ssrn.3509894
Erindi Allaj
{"title":"Realized Volatility Estimator Under Liquidity Effects","authors":"Erindi Allaj","doi":"10.2139/ssrn.3509894","DOIUrl":"https://doi.org/10.2139/ssrn.3509894","url":null,"abstract":"We analyze the behaviour of the realized volatility (RV) estimator under liquidity effects. The liquidity is measured by the impact of the trading volume on the asset price. We find that this estimator is inconsistent but convergent in probability. Motivated by this fact, we propose a new estimator which is consistent and asymptotically unbiased under a linear economy. Finally, our results are validated by a simulation and an empirical study.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116386501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Doubly Corrected Robust Variance Estimator for Linear GMM 线性GMM的双校正鲁棒方差估计
ERN: Model Construction & Estimation (Topic) Pub Date : 2019-08-12 DOI: 10.2139/ssrn.3443554
Jungbin Hwang, Byunghoon Kang, Seojeong Lee
{"title":"A Doubly Corrected Robust Variance Estimator for Linear GMM","authors":"Jungbin Hwang, Byunghoon Kang, Seojeong Lee","doi":"10.2139/ssrn.3443554","DOIUrl":"https://doi.org/10.2139/ssrn.3443554","url":null,"abstract":"We propose a new finite sample corrected variance estimator for the linear generalized method of moments (GMM) including the one-step, two-step, and iterated estimators. Our formula additionally corrects for the over-identification bias in variance estimation on top of the commonly used finite sample correction of Windmeijer (2005) which corrects for the bias from estimating the efficient weight matrix, so is doubly corrected. Formal stochastic expansions are derived to show the proposed double correction estimates the variance of some higher-order terms in the expansion. In addition, the proposed double correction provides robustness to misspecification of the moment condition. In contrast, the conventional variance estimator and the Windmeijer correction are inconsistent under misspecification. That is, the proposed double correction formula provides a convenient way to obtain improved inference under correct specification and robustness against misspecification at the same time.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130076066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
Parameter Estimation, Bias Correction and Uncertainty Quantification in the Vasicek Credit Portfolio Model Vasicek信用组合模型的参数估计、偏差校正和不确定性量化
ERN: Model Construction & Estimation (Topic) Pub Date : 2019-08-07 DOI: 10.21314/JOR.2020.429
Marius Pfeuffer, Maximilian Nagl, M. Fischer, D. Roesch
{"title":"Parameter Estimation, Bias Correction and Uncertainty Quantification in the Vasicek Credit Portfolio Model","authors":"Marius Pfeuffer, Maximilian Nagl, M. Fischer, D. Roesch","doi":"10.21314/JOR.2020.429","DOIUrl":"https://doi.org/10.21314/JOR.2020.429","url":null,"abstract":"This paper is devoted to the parameterization of correlations in the Vasicek credit portfolio model. First, we analytically approximate standard errors for value-at-risk and expected shortfall based on the standard errors of intra-cohort correlations. Second, we introduce a novel copula-based maximum likelihood estimator for inter-cohort correlations and derive an analytical expression of the standard errors. Our new approach enhances current methods in terms of both computing time and, most importantly, direct uncertainty quantification. Both contributions can be used to quantify a margin of conservatism, which is required by regulators. Third, we illustrate powerful procedures that reduce the well-known bias of current estimators, showing their favorable properties. Further, an open-source implementation of all estimators in the novel R package AssetCorr is provided and selected estimators are applied to Moody’s Default & Recovery Database.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126301315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Inference in Moment Inequality Models That Is Robust to Spurious Precision under Model Misspecification 模型不规范下矩不等式模型对伪精度的鲁棒性推断
ERN: Model Construction & Estimation (Topic) Pub Date : 2019-07-08 DOI: 10.2139/ssrn.3416831
D. Andrews, S. Kwon
{"title":"Inference in Moment Inequality Models That Is Robust to Spurious Precision under Model Misspecification","authors":"D. Andrews, S. Kwon","doi":"10.2139/ssrn.3416831","DOIUrl":"https://doi.org/10.2139/ssrn.3416831","url":null,"abstract":"Standard tests and confidence sets in the moment inequality literature are not robust to model misspecification in the sense that they exhibit spurious precision when the identified set is empty. This paper introduces tests and confidence sets that provide correct asymptotic inference for a pseudo-true parameter in such scenarios, and hence, do not suffer from spurious precision.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115661445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
The Informativeness of Estimation Moments 估计矩的信息量
ERN: Model Construction & Estimation (Topic) Pub Date : 2019-07-03 DOI: 10.1920/wp.cem.2020320
Áureo de Paula, T. Jørgensen, Bo E. Honoré
{"title":"The Informativeness of Estimation Moments","authors":"Áureo de Paula, T. Jørgensen, Bo E. Honoré","doi":"10.1920/wp.cem.2020320","DOIUrl":"https://doi.org/10.1920/wp.cem.2020320","url":null,"abstract":"This paper introduces measures for how each moment contributes to the precision of parameter estimates in GMM settings. For example, one of the measures asks what would happen to the variance of the parameter estimates if a particular moment was dropped from the estimation. The measures are all easy to compute. We illustrate the usefulness of the measures through two simple examples as well as an application to a model of joint retirement planning of couples. We estimate the model using the UK-BHPS, and we find evidence of complementarities in leisure. Our sensitivity measures illustrate that the estimate of the complementarity is primarily informed by the distribution of differences in planned retirement dates. The estimated econometric model can be interpreted as a bivariate ordered choice model that allows for simultaneity. This makes the model potentially useful in other applications.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"24 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128452297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
A Robust Approach to Heteroskedasticity, Error Serial Correlation and Slope Heterogeneity for Large Linear Panel Data Models with Interactive Effects 具有交互效应的大型线性面板数据模型的异方差、误差序列相关和斜率异质性的鲁棒方法
ERN: Model Construction & Estimation (Topic) Pub Date : 2019-06-26 DOI: 10.2139/ssrn.3215661
{"title":"A Robust Approach to Heteroskedasticity, Error Serial Correlation and Slope Heterogeneity for Large Linear Panel Data Models with Interactive Effects","authors":"","doi":"10.2139/ssrn.3215661","DOIUrl":"https://doi.org/10.2139/ssrn.3215661","url":null,"abstract":"In this paper, we propose a robust approach against heteroskedasticity, error serial correlation and slope heterogeneity for large linear panel data models. First, we establish the asymptotic validity of the Wald test based on the widely used panel heteroskedasticity and autocorrelation consistent (HAC) variance estimator of the pooled estimator under random coefficient models. Then, we show that a similar result holds with the proposed bias-corrected principal component-based estimators for models with unobserved interactive effects. Our new theoretical result justifies the use of the same slope estimator and the variance estimator, both for slope homogeneous and heterogeneous models. This robust approach can significantly reduce the model selection uncertainty for applied researchers. In addition, we propose a novel test for the correlation and dependence of the random coefficient with covariates. The test is of great importance, since the widely used estimators and/or its variance estimators can become inconsistent when the variation of coefficients depends on covariates, in general. The finite sample evidence supports the usefulness and reliability of our approach.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126628492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
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